Question

The cost to run an ad in a newspaper are given in the table. Write an equation in slope intercept form and find the cost of an ad 10 lines long. Lines Cost ($) 3 12.50 5 17.50

Answer 1

Equation: y = 2.5x + 5

Cost: $30

Step-by-step explanation:

The equation of a line can be calculated using the following:

`y=m(x-x_1)+y_1`

Where m is the slope and it is calculated as:

`m=(y_2-y_1)/(x_2-x_1)`

Where (x1, y1) and (x2, y2) are points on the line. If we take the number of lines of the ad as x and the Cost as y, then the table gives us two points (3, 12.50) and (5, 17.50)

So, replacing (x1, y1) by ( 3, 12.50) and (x2, y2) by (5, 17.50), we get that the slope and the equation are:

`m=(17.50-12.50)/(5-3)=(5)/(2)`
`\begin{gathered} y=(5)/(2)(x-3)+12.50 \\ y=(5)/(2)x-(5)/(2)\cdot3+12.50 \\ y=(5)/(2)x-(15)/(2)+12.50 \\ y=2.5x+5 \end{gathered}`

Now, to find the cost of an ad that is 10 lines long, we need to replace x by 10 and calculated y as:

`\begin{gathered} y=2.5(10)+5 \\ y=25+5 \\ y=30 \end{gathered}`

Therefore, the cost of the ad is $30